Sometimes someone wants to show off a certain new skill or joke. But what if that skill is not very impressive, or the joke is not very good? Or what if it is a little impressive, but not enough for that person to really boast about? We might say to that person: “Well, don’t give up your day job.” It means, whatever you just said or did, it wasn’t good enough to be a professional!
It may sound like it is a rude comment, but actually most Americans just think it’s a slightly funny comment.
In the case of this cartoon, this spider’s joke isn’t funny enough to make the man laugh. He even says, “Don’t quit your day job.” It means, just keep being a spider. Don’t try to be a comedian because you’re not that funny!!